Question: Activity 2: Solve Me!
• Maria walked 2 1/2 km in the morning and 1 3/4 km in the afternoon. How far did she walk?
• A recipe needs 3/4 cup of milk. You used 1/2 cup. How much more is needed?
• A 6-meter rope is cut into pieces of 3/4 meter. How many pieces are produced?
VI. What I Have Learned
Complete the statements.
1. In adding fractions with unlike denominators, I should ____________.
2. To divide fractions, I should ____________.
3. I learned that rational numbers can be ____________.
VII. Individual Assessment
1. 1/4 + 3/4 = ____
2. 5/6 - 1/2 = ____
3. 4/7 × 7/8 = ____
4. 3/5 ÷ 9/10 = ____
5. -10 + 6 = ____
6. -4 - (-8) = ____
7. 2/3 + 1/6 = ____
8. 5/8 × 4/5 = ____
9. 3/4 ÷ 1/2 = ____
10. Solve: A shirt worth ₱800 has a 1/4 discount. How much is the discount?
### Problem 1: How far did Maria walk?
1. **State the problem:** Maria walked $2 \frac{1}{2}$ km in the morning and $1 \frac{3}{4}$ km in the afternoon. Find the total distance.
2. **Convert mixed numbers to improper fractions:**
$$2 \frac{1}{2} = \frac{5}{2}, \quad 1 \frac{3}{4} = \frac{7}{4}$$
3. **Add the fractions:**
Find common denominator: $4$
$$\frac{5}{2} = \frac{5 \times 2}{2 \times 2} = \frac{10}{4}$$
$$\frac{10}{4} + \frac{7}{4} = \frac{10 + 7}{4} = \frac{17}{4}$$
4. **Convert back to mixed number:**
$$\frac{17}{4} = 4 \frac{1}{4}$$
**Answer:** Maria walked $4 \frac{1}{4}$ km in total.
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### Problem 2: How much more milk is needed?
1. **State the problem:** Recipe needs $\frac{3}{4}$ cup milk, used $\frac{1}{2}$ cup. Find how much more is needed.
2. **Subtract fractions:**
Common denominator: $4$
$$\frac{1}{2} = \frac{2}{4}$$
$$\frac{3}{4} - \frac{2}{4} = \frac{1}{4}$$
**Answer:** $\frac{1}{4}$ cup more milk is needed.
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### Problem 3: How many pieces from the rope?
1. **State the problem:** A $6$-meter rope is cut into pieces of $\frac{3}{4}$ meter. Find number of pieces.
2. **Divide total length by piece length:**
$$6 \div \frac{3}{4} = 6 \times \frac{4}{3}$$
3. **Multiply:**
$$6 \times \frac{4}{3} = \frac{6 \times 4}{3} = \frac{24}{3}$$
4. **Simplify:**
$$\frac{24}{3} = 8$$
**Answer:** $8$ pieces are produced.
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### VI. What I Have Learned
1. In adding fractions with unlike denominators, I should **find a common denominator before adding**.
2. To divide fractions, I should **multiply by the reciprocal of the divisor**.
3. I learned that rational numbers can be **expressed as fractions or decimals**.
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### VII. Individual Assessment
1. $\frac{1}{4} + \frac{3}{4} = \frac{4}{4} = 1$
2. $\frac{5}{6} - \frac{1}{2}$
Common denominator $6$:
$$\frac{1}{2} = \frac{3}{6}$$
$$\frac{5}{6} - \frac{3}{6} = \frac{2}{6} = \frac{1}{3}$$
3. $\frac{4}{7} \times \frac{7}{8} = \frac{4 \times 7}{7 \times 8} = \frac{\cancel{4}^4 \times \cancel{7}^1}{\cancel{7}^1 \times 8} = \frac{4}{8} = \frac{1}{2}$
4. $\frac{3}{5} \div \frac{9}{10} = \frac{3}{5} \times \frac{10}{9} = \frac{3 \times 10}{5 \times 9} = \frac{30}{45} = \frac{2}{3}$
5. $-10 + 6 = -4$
6. $-4 - (-8) = -4 + 8 = 4$
7. $\frac{2}{3} + \frac{1}{6}$
Common denominator $6$:
$$\frac{2}{3} = \frac{4}{6}$$
$$\frac{4}{6} + \frac{1}{6} = \frac{5}{6}$$
8. $\frac{5}{8} \times \frac{4}{5} = \frac{5 \times 4}{8 \times 5} = \frac{\cancel{5}^1 \times 4}{8 \times \cancel{5}^1} = \frac{4}{8} = \frac{1}{2}$
9. $\frac{3}{4} \div \frac{1}{2} = \frac{3}{4} \times \frac{2}{1} = \frac{3 \times 2}{4} = \frac{6}{4} = 1 \frac{1}{2}$
10. Discount on shirt worth 800 with $\frac{1}{4}$ discount:
$$800 \times \frac{1}{4} = 200$$
**Answer:** Discount is 200.